The transportation problem in linear programming is solved by a kind of simplex method in which we use a transportation tableau which corresponds to a basic solution. (See page 5 of the given link)
If we put a dot in each cell of the tableau and connect the dots which correspond to a similar row (or a similar column), a graph is made which corresponds to that basis.
How can we show that :
(a) This graph is connected.
(b) For each row and each column of the transportation tableau, there is a vertex in the graph. (This graph associated with a basis, is spanning)